7 Statistics on the DIB population

7.1 DIB distribution vs wavelength

In the previous section we discussed the identification of 226 diffuse interstellar bands in the line-of-sight of BD+63$^{\circ }$ 1964 with added confirmation in two other reddened reference targets and the possible detection of a number of others. Figures 2 and 4 show the distribution of both full widths and equivalent widths of all certain DIBs in the wavelength range of the survey. The blue end of the spectrum is characterised by both a lack of narrow DIBs and an increased abundance of broad DIBs. We rule out the possibility that this could be an instrumental bias. The lower sensitivity and increased abundance of stellar lines in the blue have already been discussed. The sensitivity limit for the survey can be estimated from the expression:

$$\sigma_{EW} = \frac{\sqrt{2 \Delta \lambda FWHM}}{\frac{S}{N}}\cdot$$

Assuming a Full Width at half maximum of typically 1 Å, for instance, we find that the sensitivity limit in the equivalent width is homogeneous from 4500 Å to 6500 Å. Applying a 5$\sigma$ confidence level would lead to the detection of DIBs with an equivalent width >12 mÅ. The equivalent width of a DIB is wavelength-dependent,

$$EW \propto Nf\lambda^{2}$$

where N is the column density of the carrier and f is the oscillator strength (Spitzer 1978). The DIBs in the red are obviously favoured. If constant column density and oscillator strength are assumed, a DIB with an equivalent width of 15 mÅ at 6000 Å would have an equivalent width of 9 mÅ at 4500 Å. This is however not sufficient to explain the lack of narrow DIBs we see in the blue. A physical explanation must be invoked to explain this phenomenon. Possible explanations might be that stronger and sharper fundamental transitions of large molecules occur in the red while secondary transitions in the blue are broadened due to limited lifetimes in excited levels of molecules (intercoupling between vibronic states). We therefore find that the survey is homogeneously complete with narrow DIBs stronger than 15 mÅ. The broader DIBs are not only concentrated towards shorter wavelengths. There is a second visible group of medium-broad to broad DIBs around 6200 Å. The pattern of DIBs also seems to involve some clustering. Five clusters of narrow DIBs, four of which gather around one or more broader ones, can be seen above 5500 Å.

7.2 Histograms of DIB widths and intensities

Figures 3 and 5 show histograms depicting the spread of both full widths and equivalent widths of DIBs measured in BD+63$^{\circ }$ 1964. We can distinguish three populations of DIBs according to their FWHM. The most abundant are those whose widths lie between 0.6 Å and 1.4 Å (narrow DIBs). Medium-broad DIBs are seen between a width of 1.4 Å and 3.2 Å, and broad DIBs, broader than 3.2 Å do not show any dominant value in the histogram. It is clear that very broad DIBs are not completely surveyed, not only due to their difficulty of detection in echelle orders, but also due to their lower contrast (for a given Equivalent Width), their blend and mutual confusion with other features. However only very clearly defined DIBs would present an interest in terms of identification. The distribution of full widths at half maximum gives direct information on physical properties of the carriers (e.g. molecular rotational contours for narrow DIBs and lifetime broadening for some of the broad DIBs).

The corresponding plot of the equivalent width distribution on the contrary (considering the statistical dispersion) does not show any preferred equivalent width above the sensitivity cut-off. This is because the equivalent width is a product of three variables, the carrier column density, N, the transition oscillator strength, f, and $\lambda^{2}$, which take a wide and continuous range of values, with independent statistics.